The "standard" scalar product on R^n is where x and y are vectors in R^n. If x and y are vectors in C^n, the scalar product is where "y*" indicates the complex conjugate of y: if then . That is, if and then the inner product of x and y is .
Hello,
I came across the following statement:
"..., where g is the complex bilinear extension of the standard scalar product on R^n to C^n (note that this a symmetric form, not a Hermitian one)."
Can someone tell me how the "complex bilinear extension" is defined, i.e. if x,y in C^n, then g(x,y)=... .
Thanks in advance!
The "standard" scalar product on R^n is where x and y are vectors in R^n. If x and y are vectors in C^n, the scalar product is where "y*" indicates the complex conjugate of y: if then . That is, if and then the inner product of x and y is .